Optimal mixture weights in multiple importance sampling
Optimal mixture weights in multiple importance sampling
复制标题
多重重要性采样中的最佳混合权重
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
A. Owen
中科院分区：
文献类型：
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作者：
Hera Y. He;A. Owen
在多重重要性抽样中，我们将来自提案分布列表的样本组合在一起。当这些提案分布被用来创建控制变量时，就有可能（Owen和Zhou， 2000）将结果方差的比例与我们列表中未知的最佳提案分布的比例绑定在一起。采用统一的提案混合会产生最大最小遗憾，但当有许多组件时，这是保守的。本文对混合成分采样率进行了优化，提高了采样效率。我们证明了控制变量混合重要性抽样的抽样方差在混合概率和控制变量回归系数中是联合凸的。我们还给出了一个顺序重要抽样算法，从样本数据中估计出最优的混合。
In multiple importance sampling we combine samples from a nite list of proposal distributions. When those proposal distributions are used to create control variates, it is possible (Owen and Zhou, 2000) to bound the ratio of the resulting variance to that of the unknown best proposal distribution in our list. The minimax regret arises by taking a uniform mixture of proposals, but that is conservative when there are many components. In this paper we optimize the mixture component sampling rates to gain further eciency. We show that the sampling variance of mixture importance sampling with control variates is jointly convex in the mixture probabilities and control variate regression coecients. We also give a sequential importance sampling algorithm to estimate the optimal mixture from the sample data.